For a non technical marketing team what is the best software for creating HTML emails that will work in most/all clients?
I am aware of MailChimp however our secondary requirement is that we can create the HTML for the email and send it to our own client list using our own software and not upload our client list to a third party.
So it sounds like you want to completely avoid using a third-party service. If that is the case, you're going to have to get your hands a little dirty (it's not that hard, really). Are you or any one on your staff familiar with basic PHP? If so, I would recommend taking a look at the following tutorial:
This describes the process of sending an e-mail from your own server using PHP.
Additionally, you might be interested in using some of the freely-available, email-optimized HTML templates that are available, for example:
Tim's answer is correct, if you want to use your own software you'll have to roll your own or use an open source product.
I would suggest this is asking for trouble. Most hosting is on a shared IP address and it is all to easy for that IP address to get added to spam blocking software.
Unless you are actively monitoring that, your deliverability could really suffer.
While I understand the desire to not upload your customer list to a third party, any reputable email provider, MailChimp, Campaign Monitor, Constant Contact would never use your data.
It's not in their best interest to do so. If they did it even once word would spread and they would loose tons of customers.
You can actually use Google Groups to send out mailings, it's free, supports rich HTML and manages subscribe / unsubscribe requests. Just create a group of each mailing list. You will of course be stuck with the third party approach.